Nonideal unilateral constraints in impulsive mechanics: a geometric approach.

We use the differential geometric framework of the first jet bundle of the classical space-time bundle to study the impulsive behavior of a mechanical system with a finite number of degrees of freedom subject to nonideal unilateral constraints. We show that this framework allows deeper insights on the concepts of nonideal constitutive characterization and of coefficient of restitution of the constraints. We study the relations among Newton, Poisson, and Stronge definitions of coefficient of restitution: we reveal the inconsistency of the criticisms based on the energy balance of the impact for the Newton definition; we show the equivalence of the three definitions in the nonideal smooth case; we prove the equivalence of Newton and Poisson ones and the insufficiency of the Stronge one in the nonideal rough case. We analyze the relation between coefficient of restitution and Coulomb’s friction coefficient in the rough case. We present also several physically meaningful examples.